Reconstruction Methods for Inverse Problems

Description

Inverse problems require to determine the cause from a set of observations. Such problems appear in medical imaging, non destructive testing of materials, computerized tomography, source reconstructions in acoustics, computer vision and geophysics, to mention but a few. Therefore their deepened mathematical study represents breakthroughs in the applications.

The primary goal of the workshop is to provide a forum on analytical and numerical aspects of the reconstruction bringing together fields, which usually do not interact. Since the field of reconstruction algorithms is wide and also because of the various links to analytical issues, we would like to mainly concentrate the workshop on the following topics

• Variational regularization methods: Tikhonov regularization, sparsity and convex constraints;
• Shape reconstruction methods: level set methods, shape derivative approach, topological gradient method and their connections;
• Iterative regularization methods: nonlinear projected steepest descent iterations linked to quantitative stability estimates.
• Bayesian approach of inverse problems and their regularization.

We envision a broad and lively discussion of all the theoretical developments, analytical and computational methodologies, new and existing applications, and growth in understanding of analysis, algorithms, and modelling.